As always, you may need to choose your initial guesses near the solutions you are looking for if you are hoping to find particular solutions. You can also try many different initial guesses to see if this can locate more than one solution.

Hi Bill,
I do appreciate your comments.
I'm looking for something where c=b. I'm working on a loop structure to build the vector FX containing the function FXi, i_1,2...N and adjust Lamda to keep up with the constraint a+d=Pmax. I did the following but I'm getting a kind of comment.

gives you a very very large random complex matrix over a,b,c,d. I could show you the particular random matrix I generated from this particular evaluation, which would take many screens here, but you can just as easily generate your own random complex matrix.

My understanding is that is equivalent to solving a system of equations made of the elements of the matrix FXlambda. Thus I think minimizing the total of the Norm of every element in FXlambda would be what I want.